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Trinity

There is one Divine Being but one indivisible essence in three persons
and the whole undivided essence belonging equally to all persons
operating and subsisting in certain and definite order. - Louis Berkhof's Systematic Theology

There are two categories of Biblical References:

Direct Reference

References that when
taken together with other similar references logically necessitates
a Trinity.

Direct References to the 3 Persons
of the Trinity:

Matthew 28:19 - Go
therefore and make disciples of all the nations, baptizing them in
the name of the Father and of the Son and of the Holy Spirit,

2 Corinthians 13:14 - The
grace of the Lord Jesus Christ, and the love of God, and the
communion of the Holy Spirit be with you all. Amen.

1 Peter 1:2 - Peter,
an apostle of Jesus Christ, To the pilgrims of the Dispersion in
Pontus, Galatia, Cappadocia, Asia, and Bithynia, 2elect according to
the foreknowledge of God the Father, in sanctification of the Spirit,
for obedience and sprinkling of the blood of Jesus Christ: Grace to
you and peace be multiplied.

John 14-16

Ephesians 2:14 - For
through Him (Jesus) we both have access by one Spirit to the Father.

1 John 5:7 - Is most
likely a 5th
century side note and therefore not inspired. Appears in Texus Reseptus (KJ and NKJ) Greek NT
because Erasmus, bowing to pressure from Rome, added it to later
editions of his Greek NT.

Indirect References:

"I wish, indeed, that such names (such as substance
and person, etc.) were buried, provided all would concur in the
belief that the Father, Son, and Spirit, are one God, and yet that
the Son is not the Father, nor the Spirit the Son, but that each has
his peculiar subsistence." - John Calvin, Institutes,
I.xiii.5

There
are six points that formulate the Biblical concept of the trinity.

The Father is God

The Son is God

The Holy Spirit is
God

The Father is not the
Son

The Son is not the
Spirit

The Father is not the
Spirit

It
might be worth pointing out that these points are formulated in the
Athanasian Creed.

The
Father is God

1 Cor. 8:6a "yet
for us there is one God, the Father, of whom are all things, and we
for Him"

John 5:31 - Father
bears witness to the Son (see law concerning 2 witnesses in Num
35:30 & Deut 17:6;19:15)

Father send the Son -
John 3:16-17, Gal 4:4, 1 John 4:10

Father loves the Son
and is well pleased with the Son - Matt 3:17, Matt 17, 2 Peter 1:17

Father and Son speak
to each other - John 11:41-42 (raising Lazarus), John 12:28 (prayer
to God in Jerusalem), John 17 (high priestly prayer)

Father and Son know
each other - Matt 11:27 (Luke 10:22) speaking to the 70 and other
passages

John 5:43 - Jesus comes in His Father's name which is contrasted with those who come in their own name, showing that the Father is not the Son.

Covenant of
redemption shows the distinction between the 1st
and 2nd person in
the Trinity.

The
Father gives the elect as a love gift to the Son

John
6:37-40 “All that the Father gives Me...”

John
10:29 “My Father who has given them(sheep) to Me...”

John 17:2-24 “...as many as You have given Him.”(vs.
2), “whom You have given Me out of the world. They were Yours, You
gave them to Me,...”(vs. 6), “I do not pray for the world but for
those whom You have given Me...”(vs. 9), “keep through Your name
those whom You have given Me.”(vs. 11), “Those whom You gave Me I
have kept..” (vs. 12), “Father, I desire that they also whom You
gave Me...” (vs. 24)

The
Son redeems the elect in obedience to the Father

John 6:39 “that of all He has given Me I should lose
nothing”

John 10:15-18 “and I lay down My life for the sheep.”,
“Therefore My Father loves Me, because I lay down My life...”

John 17:2 “that He (the Son) should give eternal life
to as many as You have given Him.”

The
Son establishes His kingdom of elect and delivers it back to the
Father in love.

1 Cor. 15:20-28, “Then comes the end, when He delivers
the kingdom to God the Father...”